Uncompressed insoluble amphiphilic molecules possessing linear hydrocarbon chains C(n)H2n+1X (n = 23, 30, 31, X = OH; n = 29, X = COOH; and n = 19, X = CONH2) spontaneously form large two-dimensional (2-D) crystalline clusters over pure water at low temperature (5-degrees-C). These 2-D crystallites were detected and their structures were solved using grazing incidence X-ray diffraction (GID). Their packing arrangements are described in terms of 2-D space-group symmetry and hydrocarbon-chain packing. All the crystal structures display rectangular unit cells containing two molecules that are probably related by glide symmetry in the 2-D space group pg for the alcohol (X = OH) and the acid (X = COOH) and by translation symmetry in the 2-D space group p1 for the amide (X = CONH2). The alcohol molecules are tilted by 8-11-degrees from the vertical toward next-nearest neighbors, the tilt angle being dependent on the chain length. The amide and the acid molecules are tilted toward nearest neighbors by 18-degrees and 26-degrees, respectively. The positional correlation lengths of the crystallites were found to be anisotropic; they extend over only 35-95 spacings parallel to the molecular tilt direction, but over 135-270 spacings perpendicular to it. The similarity of chain packing in the 2-D crystallites and in three-dimensional (3-D) crystals of aliphatic amphiphilic molecules is clearly established. These crystallites may therefore, on the water surface, mimic crystallization mechanisms observed in 3-D systems.